The application of industrial robots in the field of machining is gradually increasing, but their low absolute position accuracy and low stiffness affect the improvement of machining accuracy. Computer numerical control (CNC) has good performance to control the motion accuracy in the machine tool. Therefore, it is proposed to improve the motion accuracy of robots. This article utilizes a stereo high-speed camera to track robot motion. Circular paths running under the CNC system are planned to evaluate its performance, which includes path accuracy, motion velocity, and acceleration. The performance of identical paths running in a conventional robot controller is evaluated for comparison. Based on the experimental analysis, the CNC system, which has more functionalities for acceleration regulation, can get better path accuracy and stability. It indicates that acceleration control has a significant effect on path accuracy and motion velocity. The acceleration profile in a conventional robot controller resembles a triangle. By default, the maximum acceleration value is adopted for the motion planning. Therefore, its accelerating and decelerating phase is much shorter than that of the CNC system, which could lead to instability. Both Step-shaped and trapezoidal acceleration profiles in the CNC system improve the dynamic behavior of the robot. Considering the trade-off between path accuracy and motion velocity, the Step-shaped acceleration profile can be applied to the optimization of the traditional robot motion control.